Procedure for the estimation of parameters of a CDMA-signal

ABSTRACT

The invention concerns a procedure for the estimation of unknown parameters (Δω, Δφ, ε, g a   sync , g b   code ) of a received CDMA-signal (r dsec (v)) which is transmitted by means of a transmission channel ( 11 ), in which the CDMA-signal has experienced changes to the parameters (Δω, Δφ, ε, g a   sync , g b   code ), with the following steps: (a) formation of a cost function (L), which is dependent on the estimated values (Δ{tilde over (ω)}, Δ{tilde over (φ)}, {tilde over (ε)}, . . . ) of combined unknown parameters (Δω, Δφ, ε, . . . ); (b) partial differentiation of the cost function in respect to the said estimate values (Δ{tilde over (ω)}, Δ{tilde over (φ)}, {tilde over (ε)}, . . . ) of the unknown parameters (Δω, Δφ, ε, . . . ); (c) formation of a matrix-vector-equation from the presupposition that all partial differentials of the cost function are zero and thus a minimum of the cost function exists, and (d) computation of at least some of the matrix elements of the matrix-vector-equation with the use of the Schnellen-Hadamard-Transformation.

BACKGROUND OF THE INVENTION

[0001] The invention concerns a procedure for the estimation of theparameters of a CDMA (Code Division Multiple Access) Signal and alsoconcerns a corresponding computer program. The parameters to beestimated are, for instance, the time-shift, the frequency-shift and thephase-shift, to which the CDMA signal is subjected in the transmissionsignal and the gain factors.

[0002] As to the present state of the technology, one can refer to DE 4302 679 A1, wherein a procedure for instantaneous frequency detection fora complex base-band is disclosed. This known procedure does not,however, adapt itself to the simultaneous determination of thetime-shift and the phase-shift and further, this known procedurerequires, in the case of broadband signals, a high investment inimplementation.

[0003] All references cited herein are incorporated herein by referencein their entireties.

BRIEF SUMMARY OF THE INVENTION

[0004] Thus the invention has the purpose of creating a procedure forthe estimation of parameters of a CDMA signal and a correspondingcomputer program, which calls for a small numerical complexity and asmall cost in time and equipment, i.e., a small computational time.

[0005] The basis of the invention is, that by means of the employment ofthe Schnellen Hadamard-Transformation for computation of thecoefficients, the numerical complexity can be substantially reduced.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

[0006] An embodiment of the invention given below is described in moredetail with reference to the drawings, wherein:

[0007]FIG. 1 is a block circuit diagram of a sender-model based on theinvention procedure,

[0008]FIG. 2 is the code tree of a OVSF (Orthogonal Variable SpreadingFactor) usable in the invented procedure (Spread Codes),

[0009]FIG. 3 is the block circuit diagram of a model based on theinvented procedure of the transmission channel,

[0010]FIG. 4 is a schematic presentation to exhibit the structure of acoefficient matrix required by the numerical solution, and

[0011]FIG. 5 is a signal-flow-graph, which, with the SchnellenHadamard-Transformation employed by the invented procedure, in naturalform.

DETAILED DESCRIPTION OF THE INVENTION

[0012] In the following, the invented procedure is more closelydescribed with the aid of an example embodiment. In the case of thefollowing mathematical presentation, the following formula symbols areused: ε Time shift {circumflex over (ε)}, {tilde over (ε)} Estimatedvalue of the time shift Δω Frequency shift Δ{circumflex over (ω)},Δ{tilde over (ω)} Estimated value of the frequency shift Δθ Phase shiftΔ{circumflex over (θ)}, Δ{tilde over (θ)} Estimated value of the phaseshift ν Time Index on the chip surface c_(b) (ν) Normed capacity,unscrambled chip signal of the b-ten code channel. g_(b) ^(code) Gainfactor g_(a) ^(sync) Gain factor of the a-ten Synchornization Channel JSquare root of minus one l Time index on symbol plane n(ν) Additivedisturbance r_(desc) (ν) Unscrambled Measurement Signal r_(b) (l)Capacity normalized, undisturbed symbol of the b-ten code channel, whichuses the b-ten spread code REAL{. . .} Real Part Operator S_(desc) (ν)Unscrambled reference signal sync_(a) (ν) Capacity normalized,unscrambled chipsignal of the a-ten synchronization channel. SF_(b)Spreadfactor of the b-ten code channel w_(b) (ν) Spreadcode of the b-tencode channel x(ν) Chipsignal, which if employed for the SchnellenHadamard-Transformation. x_(b) (l) Symbol signal, as a result of theQ-ten stage of the Schellen Hadamard-Transformation. The symbols werespread with a spread code of the code class Q and the code number b.

[0013] In the following is described an estimation procedure for theapproximation of unknown parameters which exhibit a small degree ofcomplexity. This procedure is, in the case of the mobile function, thatis to say, is operable in accord with the standards 3 GPP and CDMA2000,or generally by all mobile radio systems which employ “OrthogonalVariable Spreading Factor Codes” or “Wash-codes” as a spreadingsequence. In FIG. 1, the block circuit diagram of the model of thesender 1 is based on the invented procedure. The symbols r_(b)(l) ofdifferent code channels are separated by means of orthogonal spreadingcodes w_(b)(v). The symbols r_(b)(l) and the spreading codes w_(b)(v)are spread upon the multiplier 2 _(o) to 2 _(N2). Each code channel canpossess a different gain factor g_(b) ^(code) which is fed to amultiplier 3 _(o) to 3 _(N2). As synchronization channels, unscrambledsynchronization-chip-signals sync_(a)(v) were sent which possess thegain factors g_(a) ^(sync) which are fed to the multipliers 4 _(o) to 4_(N1). The codes sync_(a)(v) of the synchronization channels are notorthogonal to the spreading codes w_(b)(v). The unscrambled referencesignal s_(desc)(V) is the sum of the signals of all N₂ code channels andthe signals of all N₁ synchronization channels and are created by theaddition units 5 and 6.

[0014] The spread code, used in the embodiment example, as these arepresented in FIG. 2, are “Orthogonal Variable Spreading Factor Codes”(OVSF) and can have their origins from different code classes. Thecode-tree is, for instance, described in more detail in T. Ojampera, R.Prasad, “Wideband CDMA for Third Generation Mobile Communications”,Artech House, ISBN 0-89006-735-x, 1998, pages 111-113.

[0015] In the WCDMA-System in accord with 3GPP in general, the summationsignal from the code channels is unscrambled by an unscrambling code.The synchronization channels are not scrambled. This fact is givenconsideration in the employed sender model, since the model describesthe generation of a unscrambled sender signal s_(desc)(v). Inconsideration of this, the synchronization channels send unscrambledcode sequences sync_(a)(v).

[0016] The model of the transmission channel 11, as shown schematicallyin FIG. 3, takes into consideration an additive disturbance n(v), anormalized time-shift on the chip period Δω and a phase-shift Δφ whichbias the scrambled reference signal, and repeats itself in themeasurement signal:

r _(desc)(v)=s _(desc)(v+ε)·e ^(+jΔω(v+ε)) ·e ^(+jΔφ) +n(v)  (1)

[0017] In the block circuit drawing are provided, on this account, twomultipliers 7 and 8, a time delay element 9 and an addition device 10.

[0018] For the in-common-estimation of all unknown parameters, that is,the timeshift ε, the frequency-shift Δω, the phase-shift Δφ and the gainfactors g_(a) ^(sync) and g_(b) ^(code) of the synchronization or codechannel, a maximum-likelihood-approximation procedure is employed, whichuses the following cost function: $\begin{matrix}{{L_{1}\left( {{\Delta \quad \overset{\sim}{\omega}},{\Delta \quad \overset{\sim}{\varphi}},\overset{\sim}{ɛ},{\overset{\sim}{g}}_{a}^{sync},{\overset{\sim}{g}}_{b}^{code}} \right)} = {\sum\limits_{v = 0}^{N - 1}{\begin{matrix}{{{r_{desc}\left( {v - \overset{\sim}{ɛ}} \right)} \cdot ^{{- {j\Delta}}\quad {\overset{\sim}{\omega} \cdot v}} \cdot ^{{- {j\Delta}}\quad \overset{\sim}{\varphi}}} -} \\{{{sync}_{a}(v)} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\overset{\sim}{g}}_{b}^{code} \cdot {c_{b}(v)}}}}\end{matrix}}^{2}}} & (2)\end{matrix}$

[0019] wherein sync_(a)(v) denotes the complex value, unscrambled,capacity normalized, undeformed chip-signal of the a-ten synchronizationchannel, also c_(b)(v) stands for the complex valued, unscrambled,capacity normalized, chip-signal of the b-ten code channelg_(a) ^(sync)of the gain factor of the a-ten synchronization channel and g_(b)^(code) represents the gain factor of the b-ten code channel.

[0020] For the minimizing of the cost function, this is linearized, inwhich process a series development of the first order of the exponentialfunction, as well as the measuring signal is used: $\begin{matrix}{{L\left( {{\Delta \quad \overset{\sim}{\omega}},{\Delta \quad \overset{\sim}{\varphi}},\overset{\sim}{ɛ},{\overset{\sim}{g}}_{a}^{sync},{\overset{\sim}{g}}_{b}^{code}} \right)} = {\sum\limits_{v = 0}^{N - 1}{\begin{matrix}{{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\overset{\sim}{\omega} \cdot v}} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad \overset{\sim}{\varphi}} - {{r_{desc}^{\prime}(v)} \cdot \overset{\sim}{ɛ}} -} \\{{\sum\limits_{a = 0}^{N_{1} - 1}{{\overset{\sim}{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\overset{\sim}{g}}_{b}^{code} \cdot {c_{b}(v)}}}}\end{matrix}}^{2}}} & (3)\end{matrix}$

[0021] The cross terms between the unknown parameters are neglected, sothat the minimizing of the cost function with a linear equation can beundertaken. This is reliable, as long as the unknown parameters aresmall, which, if necessary, can be attained by several reiterations.This means that the here presented method can be applied only for themore refined approximating.

[0022] For the computation of the partial derivatives of the linearizedcost function in accord with the unknown parameters, the followingformulations are employed: An unknown parameter x is a real valuenumber, the constants c and d are complex numbers and a cost functionemployed as a squared amount:

L=|c·x+d| ²=(c·x+d)·(c·x+d)*=|c| ² ·x ² +c*·d·x+c·d*·x+|d| ²  (4)

[0023] Now, the partial differential may be computed: $\begin{matrix}{\frac{\partial L}{\partial x} = {{2 \cdot {c}^{2} \cdot x} + {{2 \cdot {REAL}}{\left\{ {c \cdot d^{*}} \right\}.}}}} & (5)\end{matrix}$

[0024] With equation 5, the partial derivative with respect to thefrequency shift to: $\begin{matrix}{\frac{\partial L}{{\partial\Delta}\quad \hat{\omega}} = {{{2{\sum\limits_{v = 0}^{N - 1}{{{{r_{desc}(v)}}^{2} \cdot v^{2} \cdot \Delta}\quad \hat{\omega}}}} + {2{\sum\limits_{v = 0}^{N - 1}{{REAL}\left\{ {{- j} \cdot {r_{desc}(v)} \cdot v \cdot {a_{0}^{*}(v)}} \right\}}}}} = 0}} & (6)\end{matrix}$

[0025] with the following $\begin{matrix}{{{{a_{0}(v)} = {{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad \hat{\varphi}} - {{r_{desc}^{\prime}(v)} \cdot \hat{ɛ}} - {\sum\limits_{a = 0}^{N_{1} - 1}{{\hat{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\hat{g}}_{b}^{code} \cdot {c_{b}(v)}}}}},}\quad} & (7)\end{matrix}$

[0026] the partial derivative with respect to the phase shift, to$\begin{matrix}{\frac{\partial L}{{\partial\Delta}\quad \hat{\varphi}} = {{{2{\sum\limits_{v = 0}^{N - 1}{{{{r_{desc}(v)}}^{2} \cdot \Delta}\quad \hat{\varphi}}}} + {2{\sum\limits_{v = 0}^{N - 1}{{REAL}\left\{ {{- j}\quad {{r_{desc}(v)} \cdot {a_{1}^{*}(v)}}} \right\}}}}} = 0}} & (8)\end{matrix}$

[0027] with $\begin{matrix}\begin{matrix}{{a_{1}(v)} = \quad {{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\hat{\omega} \cdot v}} - {{r^{\prime}(v)} \cdot \hat{ɛ}} - {\sum\limits_{a = 0}^{N_{1} - 1}{{\hat{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} -}} \\{\quad {{\sum\limits_{b = 0}^{N_{2} - 1}{{\hat{g}}_{b}^{code} \cdot {c_{b}^{\prime}(v)}}},}}\end{matrix} & (9)\end{matrix}$

[0028] the partial derivative with respect to the time shift, to$\begin{matrix}{\frac{\partial L}{\partial\hat{ɛ}} = {{{2{\sum\limits_{v = 0}^{N - 1}{{{{r_{desc}^{\prime}(v)}}^{2} \cdot \Delta}\quad \hat{v}}}} + {2{\sum\limits_{v = 0}^{N - 1}{{REAL}\left\{ {{- {r_{desc}^{\prime}(v)}} \cdot {a_{2}^{*}(v)}} \right\}}}}} = 0}} & (10)\end{matrix}$

[0029] with $\begin{matrix}\begin{matrix}{{a_{2}(v)} = \quad {{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\hat{\omega} \cdot v}} - {j\quad {{r_{desc}^{\prime}(v)} \cdot \Delta}\quad \hat{\varphi}} -}} \\{\quad {{{\sum\limits_{a = 0}^{N_{1} - 1}{{\hat{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{{\hat{g}}_{b}^{code} \cdot c_{b}}(v)}}},}}\end{matrix} & (11)\end{matrix}$

[0030] the partial derivative, with respect to the gain factors of thesynchronization channels, to $\begin{matrix}{\frac{\partial L}{\partial{\hat{g}}_{\mu}^{sync}} = {{{2{\sum\limits_{v = 0}^{N - 1}{{{{sync}_{\mu}(v)}}^{2} \cdot {\hat{g}}_{\mu}^{sync}}}} + {2{\sum\limits_{v = 0}^{N - 1}{{REAL}\left\{ {{- {{sync}_{\mu}(v)}} \cdot {a_{3}^{*}(v)}} \right\}}}}} = 0}} & (12)\end{matrix}$

[0031] with $\begin{matrix}{{a_{3}(v)} = {{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\hat{\omega} \cdot v}} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad \hat{\varphi}} - {{r_{desc}^{\prime}(v)} \cdot \hat{ɛ}} - {\sum\limits_{a = 0}^{N_{1} - 1}{{\hat{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\hat{g}}_{b}^{code} \cdot {c_{b}(v)}}}}} & (13)\end{matrix}$

[0032] and the partial derivatives with respect to the gain factors ofthe code channels to $\begin{matrix}{\frac{\partial L}{\partial{\hat{g}}_{\mu}^{code}} = {{{2{\sum\limits_{v = 0}^{N - 1}{{{c_{\mu}(v)}}^{2} \cdot {\hat{g}}_{\mu}^{code}}}} + {2{\sum\limits_{v = 0}^{N - 1}{{REAL}\left\{ {{- {c_{\mu}(v)}} \cdot {a_{4}^{*}(v)}} \right\}}}}} = 0}} & (14)\end{matrix}$

[0033] with $\begin{matrix}{{a_{4}(v)} = {{r_{desc}(v)} = {{j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\hat{\omega} \cdot v}} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad \hat{\varphi}} - {{r_{desc}^{\prime}(v)} \cdot \hat{ɛ}} - {\sum\limits_{a = 0}^{N_{1} - 1}{{\hat{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\hat{g}}_{b}^{code} \cdot {c_{b}(v)}}}}}} & (15)\end{matrix}$

[0034] The equations (12, 13) and the equations (14, 15) are valid forall synchronization channels or for all code channels. The equations (6,7), (8, 9), (10, 11), (12, 13), (14, 15) can be summarized in amatrix-vector statement: $\begin{matrix}{{\begin{bmatrix}A_{0,0} & \quad & A_{0,{3a}} & A_{0,{4b}} \\\quad & ⋰ & \quad & \quad \\A_{{3a},0} & \quad & A_{{3a},{3a}} & A_{{3a},{4b}} \\A_{{4b},0} & \quad & A_{{4b},{3a}} & A_{{4b},{4b}}\end{bmatrix} \cdot \begin{bmatrix}{\Delta \quad \hat{\omega}} \\{\Delta \quad \hat{\varphi}} \\\hat{ɛ} \\{\hat{g}}_{a}^{sync} \\{\hat{g}}_{b}^{code}\end{bmatrix}} = \begin{bmatrix}b_{0} \\\vdots \\b_{3a} \\b_{4b}\end{bmatrix}} & (16)\end{matrix}$

[0035] whereby, the coefficients of the first row come to:

b_(a=0)  (17) $\begin{matrix}{A_{0,0} = {\sum\limits_{v}{{{r_{desc}(v)}}^{2} \cdot v^{2}}}} & (18)\end{matrix}$

$\begin{matrix}{A_{0,1} = {\sum\limits_{v}{{{r_{desc}(v)}}^{2} \cdot v}}} & (19) \\{A_{0,2} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot {r_{desc}^{\prime*}(v)} \cdot v} \right\}}}} & (20) \\{A_{0,{3a}} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot v \cdot {{sync}_{a}^{*}(v)}} \right\}}}} & (21) \\{{A_{0,{4b}} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot v \cdot {c_{b}^{*}(v)}} \right\}}}},} & (22)\end{matrix}$

[0036] The coefficients of the second line show:

b₁₌₀ $\begin{matrix}{A_{1,0} = {\sum\limits_{v}{{{r_{desc}(v)}}^{2} \cdot v}}} & (24) \\{A_{1,1} = {\sum\limits_{v}{{r_{desc}(v)}}^{2}}} & (25) \\{A_{1,2} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot {r^{\prime*}(v)}} \right\}}}} & (26) \\{{A_{1,{3a}} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot {{sync}_{a}^{*}(v)}} \right\}}}}{{A_{1,{4b}} = {\sum\limits_{v}{{REAL}\left\{ {j \cdot {r_{desc}(v)} \cdot {c_{b}^{*}(v)}} \right\}}}},}} & (27)\end{matrix}$

[0037] The coefficients of the third row show: $\begin{matrix}{b_{2} = {\sum\limits_{v}{{REAL}\left\{ {{r_{desc}^{\prime}(v)} \cdot {r_{desc}^{*}(v)}} \right\}}}} & (29) \\{A_{2,0} = {\sum\limits_{v}{{REAL}\left\{ {{- j} \cdot {r_{desc}^{\prime}(v)} \cdot {r_{desc}^{*}(v)} \cdot v} \right\}}}} & (30) \\{A_{2,1} = {\sum\limits_{v}{{REAL}\left\{ {{- j} \cdot {r_{desc}^{\prime}(v)} \cdot {r_{desc}^{*}(v)}} \right\}}}} & (31) \\{A_{2,2} = {\sum\limits_{v}{{r_{desc}^{\prime}(v)}}^{2}}} & (32) \\{A_{2,{3a}} = {\sum\limits_{v}{{REAL}\left\{ {{r_{desc}^{\prime}(v)} \cdot {{sync}_{a}^{*}(v)}} \right\}}}} & (33) \\{{A_{2,{4b}} = {\sum\limits_{v}{{REAL}\left\{ {{r_{desc}^{\prime}(v)} \cdot {c_{b}^{*}(v)}} \right\}}}},} & (34)\end{matrix}$

[0038] The coefficients of the fourth row show, $\begin{matrix}{b_{3a} = {\sum\limits_{v}{{REAL}\left\{ {{{sync}_{a}(v)} \cdot {r_{desc}^{*}(v)}} \right\}}}} & (35) \\{A_{{3a},0} = {\sum\limits_{v}{{REAL}\left\{ {{- {{sync}_{a}(v)}} \cdot j \cdot {r_{desc}^{*}(v)} \cdot v} \right\}}}} & (36) \\{A_{{3a},1} = {\sum\limits_{v}{{REAL}\left\{ {{- {{sync}_{a}(v)}} \cdot j \cdot {r_{desc}^{*}(v)}} \right\}}}} & (37) \\{A_{{3a},2} = {\sum\limits_{v}{{REAL}\left\{ {{{sync}_{a}(v)} \cdot {r_{desc}^{\prime*}(v)}} \right\}}}} & (38)\end{matrix}$

$\begin{matrix}{A_{{3a},{3\mu}} = {\sum\limits_{v}{{REAL}\left\{ {{{sync}_{a}(v)} \cdot {{sync}_{\mu}^{*}(v)}} \right\}}}} & (39) \\{A_{{3a},{4b}} = {\sum\limits_{v}{{REAL}\left\{ {{{sync}_{a}(v)} \cdot {c_{b}^{*}(v)}} \right\}}}} & (40)\end{matrix}$

[0039] and the coefficients of the fifth row are $\begin{matrix}{b_{4b} = {\sum\limits_{v}{{REAL}\left\{ {{c_{b}(v)} \cdot {r_{desc}^{*}(v)}} \right\}}}} & (41) \\{A_{{4b},0} = {\sum\limits_{v}{{REAL}\left\{ {{- {c_{b}(v)}} \cdot j \cdot {r_{desc}^{*}(v)} \cdot v} \right\}}}} & (42) \\{A_{{4b},1} = {\sum\limits_{v}{{REAL}\left\{ {{- {c_{b}(v)}} \cdot j \cdot {r_{desc}^{*}(v)}} \right\}}}} & (43) \\{A_{{4b},2} = {\sum\limits_{v}{{REAL}\left\{ {{c_{b}(v)} \cdot {r_{desc}^{\prime*}(v)}} \right\}}}} & (44) \\{A_{{4b},{3a}} = {\sum\limits_{v}{{REAL}\left\{ {{c_{b}(v)} \cdot {{sync}_{a}^{*}(v)}} \right\}}}} & (45) \\{A_{{4b},{4\mu}} = {\sum\limits_{v}{{REAL}\left\{ {{c_{b}(v)} \cdot {c_{\mu}^{*}(v)}} \right\}}}} & (46)\end{matrix}$

[0040] to the codes of the synchronization channels. Because of theorthogonal characteristic of the code channels, the coefficientsA_(4b,4μ) for b=μ equal zero. The structure of the matrix A is presentedin FIG. 4.

[0041] For the computation of the coefficients:

[0042] A_(0 4b), A_(1 4b), A_(2 4b), A_(3a,4b), A_(4b,0), A_(4b,1),A_(4b,2), A_(4b,3a) and b_(4b)

[0043] correlation products of the form: $\begin{matrix}{R_{x,c} = {\sum\limits_{v}{{REAL}\left\{ {{x(v)} \cdot \left\lbrack {c_{b}(v)} \right\rbrack^{*}} \right\}}}} & (47)\end{matrix}$

[0044] must be computed, whereby the signal x(v) can be one of thefollowing: x(v)=r(v), c(v)=r′(v) or x(v)=sync(v). The direct calculationof this correlation would have a high numerical complexity.

[0045] The algorithms for the estimation of all unknown parameters canbe implemented with a reduced numerical complexity, in case the gainfactors of a plurality of code channels must be estimated. In this case,the Schnelle Hadamard Transformation for the computation of thecoefficients

[0046] A_(0,4b), A_(1,4b), A_(2,4b), A_(3a,4b), A_(3a,4b), A_(4b,0),

[0047] A_(4b,1), A_(4b,2), A_(4b3a), and b_(4b) can be efficientlyemployed.

[0048] The capacity normalized, unscrambled, undistorted chip signalc_(b)(l·SF_(b)+v)=r_(b)(l)·w_(b)(v) (48) of a code/channel emerges fromthe spreading of the symbol r_(b)(l) of the code channel with itsspreading code w_(b)(v). The magnitude of SF_(b) presents the spreadingfactor of the code channel.

[0049] The equation (47) and the equation (48) can be brought togetherin the expression: $\begin{matrix}{R_{x,c} = {{\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {\sum\limits_{v}{{x\left( {{l \cdot {SF}_{b}} + v} \right)} \cdot {w_{b}(v)}}}} \right\}}} = {\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {x_{b}(l)}} \right\}}}}} & (49)\end{matrix}$

[0050] The inner sum from equation (49) can now be computed efficientlyfor all codes in a code class with the SchnellenHadamard-Transformation, so that the cross-correlation-coefficients nowneed only to be computed on the symbol plane.

[0051] In FIG. 5 is presented the signal flow sheet of a SchnellenHadamard-Transformation of the natural form of the length four. Thechip-signal x(v) transformed in the first stage of the transformation inthe code class CC=1. The results in the first stage of thetransformation, x₀(l+0), x₁(l+0), x₀(l+1) and x₁(l+1), represent theinner sum of the equation 49 for the code channels, which the spreadingcodes from the code class CC=1 employ. In the second stage of thetransformation, one obtains the results of the inner summation ofequation (49) for the code channels, which the spreading code uses fromthe code class CC-2.

[0052] The numerical complexity lessens, because, first, the SchnellenHadamard-Transformation possesses a complexity of M·log M in comparisonto the complexity of the direct computation with equation (49) of M².Further, in the computation of the inner summation of equation (49) onlytwo real value signals must be considered, and it need not, as is thecase with the direct computation from equation (47) be carried out bycomputations with complex valued signals.

[0053] While the invention has been described in detail and withreference to specific examples thereof, it will be apparent to oneskilled in the art that various changes and modifications can be madetherein without departing from the spirit and scope thereof.

What is claimed is:
 1. A process for estimating unknown parameters (Δω,Δφ, ε, . . . ) of a received CDMA signal (r_(desc)(v)), which is sent bymeans of a transmission channel, in which the CDMA-signal hasexperienced changes of the parameters (Δω, Δφ, ε, . . . ), the processcomprising: formation of a cost function (L), which is dependent onestimated values (Δ{tilde over (ω)}, Δ{tilde over (φ)}, {tilde over(ε)}, . . . ) of combined unknown parameters (Δω, Δφ, ε, . . . ),partial differentiation of the cost function in respect to the estimatevalues (Δ{tilde over (ω)}, Δ{tilde over (φ)}, {tilde over (ε)}, . . . )of the unknown parameters (Δω, Δφ, ε, . . . ), formation of amatrix-vector-equation from a presupposition that all partialdifferentials of the cost function are zero and thus a minimum of thecost function exists, and computation of at least some of the matrixelements of the matrix-vector-equation with aSchnellen-Hadamard-Transformation.
 2. The process of claim 1, wherein:CDMA-signals are from chip-signals c_(b)(v) of a plurality of codechannels, which, are multiplied by different, orthogonal spreading codesw_(b)(v) and are multiplied by different gain factors g_(b) ^(code), andat least one chip-signal sync_(a)(v), at least one synchronizationchannel, which is multiplied by a gain factor g_(a) ^(sync), iscombined, and unknown parameters of the received CDMA signal are: thetime shift ε, the frequency shift Δω, the phase shift Δφ and the gainfactors g_(b) ^(code) and g_(a) _(sync) of the code channels and the atleast one synchronization channels.
 3. The process of claim 2, whereinthe chip-signal sync_(a)(v) of each synchronization channel isunscrambled.
 4. The process of claim 2, wherein the following costfunction L₁ is formed:${L_{1}\left( {{\Delta \quad \overset{\sim}{\omega}},{\Delta \quad \overset{\sim}{\varphi}},\overset{\sim}{ɛ},{\overset{\sim}{g}}_{a}^{sync},{\overset{\sim}{g}}_{b}^{code}} \right)} = {\sum\limits_{v = 0}^{N - 1}{{{{r_{desc}\left( {v - \overset{\sim}{ɛ}} \right)} \cdot ^{{- j}\quad \Delta \quad \overset{\sim}{\omega}v} \cdot ^{{- j}\quad \Delta \quad \overset{\sim}{\varphi}}} - {\sum\limits_{a = 0}^{N_{1} - 1}{{\overset{\sim}{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\overset{\sim}{g}}_{b}^{code} \cdot {c_{b}(v)}}}}}^{2}}$


5. The process of claim 4, wherein the cost function L₁, by means ofseries development of a first order is transposed into the followinglinearized cost function L:${L_{1}\left( {{\Delta \quad \overset{\sim}{\omega}},{\Delta \quad \overset{\sim}{\varphi}},\overset{\sim}{ɛ},{\overset{\sim}{g}}_{a}^{sync},{\overset{\sim}{g}}_{b}^{code}} \right)} = {\sum\limits_{v = 0}^{N - 1}{\begin{matrix}{{r_{desc}(v)} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad {\overset{\sim}{\omega} \cdot v}} - {j\quad {{r_{desc}(v)} \cdot \Delta}\quad \overset{\sim}{\varphi}} - {{r_{desc}^{\prime}(v)} \cdot \overset{\sim}{ɛ}} -} \\{{\sum\limits_{a = 0}^{N_{1} - 1}{{\overset{\sim}{g}}_{a}^{sync} \cdot {{sync}_{a}(v)}}} - {\sum\limits_{b = 0}^{N_{2} - 1}{{\overset{\sim}{g}}_{b}^{code}{c_{b}(v)}}}}\end{matrix}}^{2}}$


6. The process of claim 5, wherein the linearized cost function L isdifferentiated with respect to the time shift ε, the frequency shift Δω,the phase shift Δφ as well as with respect to the gain factors g_(b)^(code) and g_(a) _(sync) and thereby an equation system is obtained,which can be expressed in matrix form as follows: ${\begin{bmatrix}A_{0,0} & \quad & A_{0,{3a}} & A_{0,{4b}} \\\quad & ⋰ & \quad & \quad \\A_{{3a},0} & \quad & A_{{3a},{3a}} & A_{{3a},{4b}} \\A_{{4b},0} & \quad & A_{{4b},{3a}} & A_{{4b},{4b}}\end{bmatrix} \cdot \begin{bmatrix}{\Delta \quad \hat{\omega}} \\{\Delta \quad \hat{\varphi}} \\\hat{ɛ} \\{\hat{g}}_{a}^{sync} \\{\hat{g}}_{b}^{code}\end{bmatrix}} = \begin{bmatrix}b_{0} \\\vdots \\b_{3a} \\b_{4b}\end{bmatrix}$


7. The process of claim 6, wherein the computation of the coefficients:A_(0,4b), A_(1,4b), A_(2,4b), A_(3a,4b), A_(ab,0), A,_(ab,1) A_(ab,2),A_(4b,3a) and b_(4b) the following equation is solved:$R_{x,c} = {{\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {\sum\limits_{v}{{x\left( {{{l \cdot S}\quad F_{b}} + v} \right)} \cdot {w_{b}(v)}}}} \right\}}} = {\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {x_{b}(l)}} \right\}}}}$


8. The process of claim 7, wherein an inner sum of the equation:$R_{x,c} = {{\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {\sum\limits_{v}{{x\left( {{{l \cdot S}\quad F_{b}} + v} \right)} \cdot {w_{b}(v)}}}} \right\}}} = {\sum\limits_{l}{{REAL}\left\{ {\left\lbrack {r_{b}(l)} \right\rbrack^{*} \cdot {x_{b}(l)}} \right\}}}}$

is computed for all codes in a code class with the SchnellenHadamard-Transformation
 9. A computer program with a program code forexecuting the process of claim 1 when the program is run in a computer.10. A computer program with a program code stored on a machine-readablecarrier for executing the process of claim 1 when the program is run ina computer.